Problem :
Blaise decides to build a barometer. He can't find any mercury in his
workshop and decides to use water instead. Assume that the density of water is
1.00×10^{3} kg/m^{3}. If the atmospheric pressure is 7.60×10^{2} torr, how tall must his barometer be in order to obtain an accurate
reading?
First, convert the atmospheric pressure to Pascals.
7.60×10^{2} torr = 101, 325 Pa. Now that all the variables are in SI units,
rearrange
P = ghρ to
P/(gρ) = h and plug the variables into the
equation.
= = 10.3 m 

Thus Blaise's barometer must be taller than 10.3 meters. A comparable mercury
barometer would be 0.76 m tall.
Problem :
In a fit of inspiration and hot air, you have blown the world's largest balloon.
Your two cousins, Bongo the 300 lb. gorilla and Jeeves the 70 lb. weakling, both
want to climb to the top of your balloon. When Bongo goes, he goes in style.
He wants to lay down on his 1 m by 5 m air bed at the summit. Jeeves proposes
to bounce on the top of the balloon on his pogo stick, whose head has an area of
0.001 m^{2}. Assume that the masses of the bed and pogo stick are
negligible, and that their occupants' weights are evenly distributed upon them.
You know that your balloon can sustain 200 more kPa of pressure on its surface
before it pops. Assuming both can make it to the top without damaging the
balloon (or themselves), which cousin(s) should you allow to climb?
P = F/A, so the first thing we need to do is convert everything to the
appropriate units. Let's use SI units.
1 lb = 0.454 kg, and
F = (mass)×(9.8 m/s^{2}), so Bongo and Jeeves exert forces of
1330 and 311 Newtons, respectively.
P = F/A, so Bongo has a pressure of
P_{Bongo} = = 270 Pa. Jeeves
exerts a pressure of
P_{Jeeves} = (311 N)×(0.001 m^{2}) = 310 kPa. You should allow Bongo on, but not Jeeves.
Problem :
After an interdimensional mishap, Blaise finds himself on a strange planet with
nothing but an empty barometer and a jar of alien liquid. After working with
barometers for many years, Blaise has developed a keen sense of pressure. He
reckons that the atmospheric pressure is 1.4 atmospheres. The label on
the jar claims that the density of the liquid is 1.0×10^{5}. He pours the liquid into his barometer, and
finds that the atmosphere supports a column 0.072 m tall. What is the
gravitational acceleration g on this planet?
We can rearrange the barometer equation to solve for
g:
= g 

Let's stick with SI units to keep everything consistent.
1 atm = 1.013×10^{5} Pa, so
P is 142,000 Pa. Plugging in
h and
ρ, we find that
g = 20 .